# The Lighthouse Problem

##### This The Lighthouse Problem activity & project also includes:

Long considered the symbol of safe harbor and steadfast waiting, the lighthouse gets a mathematical treatment. The straightforward question of distance to the horizon is carefully presented, followed by a look into the different interpretations of the ideas of distance. A natural application of trigonometric calculations and the relationships of circles and triangles, this activity extends even further to questions of precision and accuracy. Teaching notes and suggestions provide great insight into parts that commonly trip up learners and how to prevent / remediate these misconceptions.

CCSS: Designed

##### Instructional Ideas

• Use as an application problem after the class learns about tangent / radius relationships to provide some open-ended practice with the concepts
• Discussions of appropriate precision mesh with a science or engineering presentation on rounding and its dangers (there are several famous structures brought down by mis-applied rounding and units)
• Links to American history lessons on lighthouses and their roles in shaping historical events
##### Classroom Considerations

• Part B requires some knowledge of finding arc length in addition to the trigonometric ratios used in part A; this may be a consideration as to when the problem is usable
• Lesson points on precision and rounding might need to be emphasized to learners playing it fast and loose with the calculations
##### Pros

• Real-world application of theoretical trigonometric calculations
• Important investigation into both the precision of language and of calculations
##### Cons

• Learner activity not separated from teaching notes and answer key